Mathematical expressions in this patent specification are based upon complex equivalent baseband notation. Essentially, complex quantities are used to represent the amplitude and phase of radio signals with the effect of the carrier removed. Hence, if s1(t) is the complex baseband equivalent of bandpass modulated signal s(t) and fc is the carrier frequency, we have:s(t)=Re[s1(t)ej2πfct],  (1) where Re[·] denotes the real part of its argument and j=√{square root over (−)}1.
Array antenna radio receivers typically are employed at the base stations of digital cellular communication systems (e.g. mobile telephone networks, broadband wireless access for Internet and/or wide-area networking, etc.) to improve reception link quality (i.e. provide robustness against multipath fading) and/or reduce interference levels where interference can include thermal noise and man-made signals which exist in the desired signal's band. Since such systems typically accommodate large numbers of simultaneously active users in any given cell or cell sector, the base station receiver must be capable of maintaining a plurality of radio links.
Known antenna array radio receiver systems comprise an array of antenna elements coupled to a signal receiving apparatus (also referred to as a radio-frequency (RF) front-end) which in turn is coupled to a signal processing apparatus. The signal receiving apparatus processes the signals from the different antenna elements independently, in separate branches, and performs on each signal standard downconversion, demodulation, filtering to isolate the channel of interest and, possibly, some transformation on the signal to bring it to a form usable by the signal processing apparatus (e.g. analog-to-digital conversion if the signal processor is digital). The signal processor takes the information from all of the branches (i.e. the demodulated, filtered and suitably transformed signal data from each individual antenna element) and, using one of a number of appropriate known techniques, combines and processes it to extract a useful signal y(t), which is the best possible estimate of the desired user signal.
In the context of wireless communications, the received vector x(t) (i.e. the received signal across all array elements) is made up of a desired signal s0(t) transmitted by a wireless terminal, interfering signals s1(t) transmitted by competing terminals which operate in the same frequency band or in adjacent bands with some amount of crosstalk being present, and white noise. Hence                               x          ⁡                      (            t            )                          =                                                            c                0                            ⁡                              (                t                )                                      ⁢                                          s                0                            ⁡                              (                t                )                                              +                                    ∑                              i                =                1                            M                        ⁢                                                   ⁢                                                            c                  i                                ⁡                                  (                  t                  )                                            ⁢                                                s                  i                                ⁡                                  (                  t                  )                                                              +                      n            ⁡                          (              t              )                                                          (        2        )            where c1(t) is an N×1 vector of complex elements describing the channels from the ith terminal to all of the N array elements, M is the number of interfering signals and n(t) is the white noise vector.
In such a context, the function of the antenna array radio receiver is to isolate the desired signal s0(t) from the interferers and white noise as well as compensate for distortions introduced in the channel c0(t) (e.g. multipath fading) so that, at all times, the array output y(t) approximates the desired signal s0(t) as closely as possible.
Typically, the combination of the signals from the individual elements is simply a linear weight-and-sum operation. If an N-element array is considered and x(t) is the N×1 vector of the array element outputs, the array output is defined asy(f)=w(t)Hx(t),  (3) where w(t) is the N×1 complex weight vector and (·)H denotes the hermitian transpose (i.e. complex conjugate transpose) of its argument, be it a vector (as it is in the above) or a matrix. Although it is time-varying, the weight vector varies slowly compared to the input and output signals. When a combiner operates according to equation (3), it is termed a linear combiner and the entire receiver is designated a linear array receiver.
Given an N-element linear array, it is theoretically possible to null up to N−1 interferers although at the cost of some degree of noise enhancement. However, arrays can also be employed to provide a diversity gain against multipath fading (since deep fades will rarely occur on more than one branch at a time provided that the antenna elements are spaced sufficiently apart). It is known that a K+M-element array can null up to M−1 interferers while providing a diversity improvement of order K+1 against multipath fading. It is also known that an optimum combiner (described below) implicitly allocates degrees-of-freedom (DOFs) to interference rejection first. Leftover DOFs, if any, are employed to combat fading.
Typically, the receiver collects statistics of the input signal and uses them to derive a weight vector which minimizes some error measure between the array output y(t) and the desired signal s0(t). The most common error measurement is the mean-square errorε=<[y(t)−s0(t)]2>=<[wH(t)x(t)−s0(t)]2>,  (4) which forms an N-dimensional quadratic surface with respect to the weight vector elements. It thus has a single global minimum. The minimization of this criterion forms the basis of mean-square-error (MSE) minimizing linear array receivers or, equivalently, minimum mean-square-error (MMSE) linear array receivers (also called optimum combiners). (In the following equation (5), and others to follow, the dependence upon t is omitted for the sake of clarity.) Adaptive filtering theory indicates that the best combination of weights for a given sequence of received data is given byw=Rxx−1c0,  (5) where Rxx is the covariance matrix of the received array outputs and is given byRxx=<x(t)xH(t)>,  (6) where (·) denotes the expectation (i.e., the ensemble average) of its argument.
Such array receivers are suitable for use where time dispersion due to multipath propagation does not extend significantly beyond a single symbol period. That is, there is little or no intersymbol interference (ISI).
When the channels carrying useful signals do exhibit significant ISI, the traditional solution is to use an equalizer, which is an adaptive filter whose purpose is to invert the channel impulse response (thus untangling the ISI) so that the overall impulse response at its output will tend to have an ideal, flat (or equalized) frequency spectrum.
The signal processing portion of the standard linear equalizer works in the same way as a linear adaptive array receiver except that the signal sources are not points in space (i.e., the array of antenna elements) but points in time. The signals are tapped at a series of points along a symbol-spaced delay line (termed a tapped delay line or TDL), then weighted and combined.
While the implementation of the signal processing apparatus for both equalizer and array receiver can be identical (minimization of the MSE by adaptive weighting of the inputs) the performance will differ. Because signals are physically sampled at different points in space by the array receiver, it is very effective at nulling unwanted signal sources or co-channel interference (CCI). However, it has limited ability against intersymbol interference (ISI) due to dispersive, i.e., frequency-selective, fading, since the latter is spread in time. On the other hand, the equalizer is adept at combatting ISI but has limited ability against CCI.
In environments where both ISI and CCI are present, array reception and equalization may be combined to form a space-time processor. The most general form of the latter is obtained when each weighting multiplier in a narrowband array is replaced by a full equalizer for a total of N equalizers. Again, the implementation of the signal processing apparatus will be identical and will rely on equation (3) supra. The only difference is that the weight vector w and the input vector x will be longer. Indeed, for an equalizer length of L taps and an array size of N elements, the vectors w and x will both have LN elements.
The canonical linear mean-square-error minimizing space-time receiver (i.e. the most obvious and immediate linear space-time receiver structure and also in certain respects the most complex) comprises an antenna array where each array element output is piped to a finite impulse response (FIR) adaptive filter, which in this context is referred to as an equalizer. Each adaptive filter comprises a tapped-delay line having taps spaced by a symbol period or a fraction of a symbol period. For good performance, the length of the tapped-delay line should be equal or superior to the average channel memory length. In many cases, the number of taps this implies can be very large (e.g. 10-100 per adaptive filter). An important special case is where the channel memory length is of the order of a symbol period. The channel is then said to be flat fading and the adaptive filters in each branch are reduced to a single weighting complex multiplier. This simplified structure is termed a narrowband array or spatial processor.
On the other hand, if the channel memory length is more than a single symbol period, the channel is subjected to frequency-selective fading (also called time dispersive or simply dispersive fading) thus inducing intersymbol interference (ISI) at the receiver. Such a situation requires the more general structure with a complete adaptive filter per branch; such a system is variously designated as wideband array or space-time processor.
The weights multiplying each tap output must be constantly adapted to follow the changes in the characteristics of the desired user's and interferers' channels. In a representative class of such systems, the weights are computed on a block-by-block basis (block adaptation) and each block contains a training sequence of known training symbols for that purpose. In digital wireless communications systems, the block used for adaptation purposes will typically correspond to a data packet as defined by the networking protocol in use.
By adapting the weights to minimize a global performance index, i.e. the mean-square error between the desired signal and the S-T receiver output, the receiver implicitly performs the following:                reduces or eliminates intersymbol interference (ISI) caused by frequency-selective fading in wideband channels;        reduces or eliminates co-channel interference (CCI) from nearest cells where carriers are reused or from inside the cell, since the space-time processor permits reuse of carriers within the cell or the sector thanks to its power of spatial discrimination—often referred to as Space Division Multiple Access (SDMA).        improves output SNR (due to the array's larger effective aperture).        
The number of temporal elements depends primarily upon the degree of intersymbol interference and could be between say, 10 and 100. The number of spatial elements depends upon the number of antenna elements and could be, say, 10. The number of antenna elements is chosen as a function of the maximum number of interferers to be nulled and the desired gain against fading.
Since wireless systems are typically interference-limited (i.e., interference is the main impediment which prevents capacity increase—accommodating more active users—above a certain limit), the first two benefits of space-time processors are of most interest in order to increase capacity To achieve maximal benefit, it is better to combine the array with carrier reuse-within-cell (RWC), also called space-division multiple access (SDMA). In known such systems, separate S-T processors will have to be implemented for every user (all processors share the same physical antenna array and front-end receiver circuitry but have distinct equalizers and combiners). This can result in a prohibitively complex receiver system from a numerical and/or hardware complexity standpoint, especially if the memory length L of the channels is large and regardless of whether RWC is used or not. Therefore, it is of great relevance to develop reduced-complexity space-time receiver architectures.
It is known to reduce complexity and/or hardware requirements of an array receiver by using a single RF receiver and selecting different antenna elements in turn. This is termed selection diversity and it provides some gain against multipath fading but, in general, little or no gain against CCI.
It is also known to do so by selecting a subset of the signals from the antenna elements, for each user, and processing those.
In the context of wireless communications, when a remote station transmits a signal to the array antenna, multipath effects will result in destructive/constructive interference, so the signals in each branch, i.e., extracted from the different antenna elements, will have different signal-to-noise ratios. Also, the signal may be strongest in a certain angular sector or cone, depending upon the configuration of the antenna array. Indeed, little scattering occurs in the immediate vicinity of an elevated base station such that most received energy will typically be concentrated in a narrow angle around a single main direction of arrival.
It is known, therefore, to select and process only a subset of the signals comprising those with the highest signal-to-noise ratio, as disclosed, for example, in an article entitled “SNR of Generalized Diversity Selection Combining with Nonidentical Rayleigh Fading Statistics” by N. Kong and L. B. Milstein, IEEE Transactions on Communications, Vol. 48, No. 8, pp. 1266-1271, August 2000. A disadvantage of these techniques is that they base the subset selection upon instantaneous measured power in each branch, which still entails a significant amount of hardware complexity and/or computational overhead. Indeed, while only as many complete RF front-ends as subset elements may be required, all array elements must be monitored at all times, possibly using a plurality of signal power measurement devices. Moreover, a software-radio-type implementation will require the processor to poll the said measurement devices frequently thus introducing undesirable overhead.
A further disadvantage of such known techniques is that they do not differentiate between interference from other users and white noise It is possible that a subset of branch signals with the highest individual signal-to-noise ratios, when combined, will not perform as well as a different subset in which one or more of the branch signals have lower individual signal-to-noise ratios. For example, the latter subset of signals might involve interferers whose signals tend to negate each other so that, when combined, they produce a better overall signal quality.
U.S. Pat. No. 6,081,566 issued Jun. 27, 2000 by Molnar et al. discloses a receiver which bases subset selection upon a number of criteria including signal quality as measured from signal power and so-called “impairment power”. This is not entirely satisfactory, however, because the signal quality measurement still is computed for each individual branch and so could still result in a sub-optimum subset being selected.